Trinita for a nice change to Rewe and co. you can go to Stelios Supermarket on Wilhelmsplatz 7. It's a kind of Mediterranean supermarket with everything from meat, fish, pasta, olives etc etc. Very simple shop, but good.
Specialised shop for flour is a tricky question. Not sure about what to say. I'd probably try Edeka in Frankfurt Ostend. Huge supermarket with an amazing selection of everything. There you will probably find 10 different kinds of wheat flours in the shelf. Worth the trip over the river. One of the best supermarkets in Rhein-Main. Otherwise you might want to try Tegut in Komm Center in Offenbach. They also have a decent selection. Or you got to Alnatura in Offenbach Hafen. Small but specialised selection of products. All these places are actually good and you should know if you live in OF.